There are a variety of simulations of waves in a stretched string.

 

• This simulation from Andrew Duffy at Boston University illustrates standing and traveling waves in a string, and harmonics.

http://physics.bu.edu/~duffy/HTML5/transverse_standing_wave.html

 

• This simulation from Falstad illustrates standing waves on a string, with a breakdown of fourier harmonic magnitudes and phases. You can show the results from a transient plucking or an ongoing driving force, with variable tension and damping.

http://www.falstad.com/loadedstring/

 

• Dan Russell of Penn State offers animations and mathematical treatments of plucked, struck/hammered, and bowed strings.

Plucked (e.g. guitar): http://www.acs.psu.edu/drussell/Demos/Pluck-Fourier/Pluck-Fourier.html

Struck (e.g. piano): http://www.acs.psu.edu/drussell/Demos/StruckString/Struck-Fourier.html

Bowed (E.g. violin): http://www.acs.psu.edu/drussell/Demos/Bowed-String/Bowed-String.html

 

• Russell also offers this comparison of strings and 2D membranes

https://www.acs.psu.edu/drussell/Demos/Membrane-vs-String/Membrane-vs-String.html